Finite-Temperature Field Theory

Kapusta, Joseph I.; Landshoff, P.V.

doi:10.1017/cbo9780511535130

Cited by 1,422 publications

(1,589 citation statements)

References 11 publications

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“…Moreover, since H is time independent, the temporal part of the functional trace in Eq. (18) can be evaluated in the usual way by summing fermionic Matsubara frequencies [70]. One obtains…”

Section: Mean-field Approximationmentioning

confidence: 99%

Inhomogeneous chiral condensates

Buballa

Carignano

2015

Progress in Particle and Nuclear Physics

247

258

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The chiral condensate, which is constant in vacuum, may become spatially modulated at moderately high densities where in the traditional picture of the QCD phase diagram a first-order chiral phase transition occurs. We review the current status of this idea, which originally dates back to Migdal's pion condensation, but recently received new momentum through studies on the nature of the chiral critical point and by the conjecture of a quarkyonic-matter phase. We discuss how these nonuniform phases emerge in generalized Ginzburg-Landau analyses as well as in specific calculations, both within effective models and in Dyson-Schwinger or large-N c approaches to QCD. Questions about the most favored shape of the modulations and its dimension, and about the effects of nonzero isospin chemical potential, strange quarks, color superconductivity, and external magnetic fields on these inhomogeneous phases will be addressed as well.

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“…Moreover, since H is time independent, the temporal part of the functional trace in Eq. (18) can be evaluated in the usual way by summing fermionic Matsubara frequencies [70]. One obtains…”

Section: Mean-field Approximationmentioning

confidence: 99%

Inhomogeneous chiral condensates

Buballa

Carignano

2015

Progress in Particle and Nuclear Physics

247

258

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“…In the case of static potential model, where V does not depend explicitly on the Matsubara frequency, one can evaluate the sum analytically [6]. Performing the sum over ω n = (n+ 1 2 ) 2π β , we arrive at the gap equations:…”

Section: Gap Equations At Finite Temperaturementioning

confidence: 99%

“…In finite temperature field theory [6,7], one is concerned with the calculation of the thermal average of an observable. The partition function is defined as…”

Section: Introduction To Finite Temperature Field Theorymentioning

confidence: 99%

Confinement models at finite temperature and density

Swanson

2010

Phys. Rev. D

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This work presents a non-perturbative study of dynamical chiral symmetry breaking in various confinement models at finite temperature and density. The tool of choice is the Schwinger-Dyson equations. We shall discuss (i) the inadequacy of static confinement models in explaining thermal properties of QCD (ii) dynamical chiral and parity symmetry breaking of three dimensional QED with two-component fermions (iii) endemic infrared divergences in QED3 at finite temperature and the attempt to solve the system self-consistently.

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“…Usually one performs a standard one-loop calculation assuming a homogeneous and static background field [12]. Nevertheless, for a system that is in the process of phase conversion after a chiral transition, one expects inhomogeneities in the chiral field configuration due to fluctuations to play a major role in driving the system to the true ground state.…”

Section: Abstract: Chiral Symmetry Breakingmentioning

confidence: 99%

Nucleation in the chiral transition with an inhomogeneous background

Taketani¹,

Fraga²

2007

Braz. J. Phys.

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We consider an approximation procedure to evaluate the finite-temperature one-loop fermionic density in the presence of a chiral background field which systematically incorporates effects from inhomogeneities in the chiral field through a derivative expansion. Modifications in the effective potential and their consequences for the bubble nucleation process are discussed. Keywords: Chiral symmetry breakingThe mechanism of chiral symmetry breaking and the study of the dynamics of phase conversion after a temperaturedriven chiral transition can be done conveniently within lowenergy effective models [1][2][3][4][5][6][7][8][9]. In particular, to study the mechanisms of bubble nucleation and spinodal decomposition in a hot expanding plasma [10], it is common to adopt the linear σ-model coupled to quarks [11]. The gas of quarks provides a thermal bath in which the long-wavelength modes of the chiral field evolve, and the latter plays the role of an order parameter in a Landau-Ginzburg approach to the description of the chiral phase transition. The standard procedure is then integrating over the fermionic degrees of freedom, using a classical approximation for the chiral field, to obtain a formal expression for the thermodynamic potential from which one can obtain all the physical quantities of interest.To compute correlation functions and thermodynamic quantities, one has to evaluate the fermionic determinant that results from the functional integration over the quark fields within some approximation scheme. Usually one performs a standard one-loop calculation assuming a homogeneous and static background field [12]. Nevertheless, for a system that is in the process of phase conversion after a chiral transition, one expects inhomogeneities in the chiral field configuration due to fluctuations to play a major role in driving the system to the true ground state. In fact, for high-energy heavy ion collisions, hydrodynamical studies have shown that significant density inhomogeneities may develop dynamically when the chiral transition to the broken symmetry phase takes place [6], and inhomogeneities generated during the late stages of the nonequilibrium evolution of the order parameter might leave imprints on the final spatial distributions and even on the integrated, inclusive abundances [13].In this paper we briefly describe an approximation procedure to evaluate the finite-temperature fermionic density in the presence of a chiral background field, which systematically incorporates effects from inhomogeneities in the bosonic field through a gradient expansion. (For details, see Ref. [14].) The method is valid for the case in which the chiral field varies smoothly, and allows one to extract information from its long-wavelength behavior, incorporating corrections order by order in the derivatives of the field. For simplicity, we ignore corrections coming from bosonic fluctuations in what follows. Those would result in a bosonic determinant correction to the effective potential [15]. To focus on the effect of an inhomogeneou...

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Finite-Temperature Field Theory

Cited by 1,422 publications

References 11 publications

Inhomogeneous chiral condensates

Inhomogeneous chiral condensates

Confinement models at finite temperature and density

Nucleation in the chiral transition with an inhomogeneous background

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